{"title":"网格的素直观模糊理想的泛化","authors":"Poonam Kumar Sharma","doi":"10.7546/nifs.2024.30.1.26-55","DOIUrl":null,"url":null,"abstract":"As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"28 16","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalizations of prime intuitionistic fuzzy ideals of a lattice\",\"authors\":\"Poonam Kumar Sharma\",\"doi\":\"10.7546/nifs.2024.30.1.26-55\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.\",\"PeriodicalId\":509276,\"journal\":{\"name\":\"Notes on Intuitionistic Fuzzy Sets\",\"volume\":\"28 16\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Notes on Intuitionistic Fuzzy Sets\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/nifs.2024.30.1.26-55\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notes on Intuitionistic Fuzzy Sets","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/nifs.2024.30.1.26-55","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
作为对直觉模糊素理想和直觉模糊素理想概念的概括，引入了直觉模糊 2 吸收理想和网格的 2 吸收直觉模糊理想的概念。证明了关于这类直观模糊理想的一些结果。证明了当且仅当 L 的直观模糊理想的基是 L 的 2 吸直观模糊理想时，L 的直观模糊理想的基才是 2 吸直观模糊理想。
Generalizations of prime intuitionistic fuzzy ideals of a lattice
As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.
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